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Computing regions of interest for geometric features in digital images

Kristof Teelen, Peter Veelaert
2009 Discrete Applied Mathematics  
The focus is on the solution of transformation problems for geometric primitives, especially lines, so that regions of interest can be computed for corresponding geometric features in distinct images.  ...  We present an uncertainty model for geometric transformations based on polygonal uncertainty regions and transformation polytopes.  ...  Acknowledgments A preliminary version of this paper was presented at the 12th International Workshop on Combinatorial Image Analysis, Buffalo, NY, USA, April 2008 [9] .  ... 
doi:10.1016/j.dam.2009.02.002 fatcat:evdgd3ajdradrmzbsdqkmwrtxy

Uncertain Geometry in Computer Vision [chapter]

Peter Veelaert
2005 Lecture Notes in Computer Science  
We illustrate the use of uncertain geometry with examples involving the detection of circles and the computation of transformations between images.  ...  The statistical properties of these graphs are important when we design algorithms for the extraction of geometric primitives from images.  ...  corresponding feature point in the first image.  ... 
doi:10.1007/978-3-540-31965-8_33 fatcat:ddqxvbilibdldmutwzfrlzmsgi

A generalized preimage for the digital analytical hyperplane recognition

M. Dexet, E. Andres
2009 Discrete Applied Mathematics  
Each point in this preimage corresponds to a Euclidean hyperplane the digitization of which contains all given hypervoxels.  ...  The principle is to incrementally compute in a dual space the generalized preimage of the ball set corresponding to a given hypervoxel set according to the chosen digitization model.  ...  Dual of a polytope In order to define the dual of a polytope, we use a dual transformation similar to the well known Hough transform which is an efficient tool usually used in image processing to recognize  ... 
doi:10.1016/j.dam.2008.05.030 fatcat:stl3ubrserh5bg32xae5irov6u

Practical solutions for counting scalars and dependences in ATOMIUM-a memory management system for multidimensional signal processing

F. Balasa, F. Catthoor, H.J. De Man
1997 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Index Terms-Data dependence, data-flow analysis, digital signal processing (DSP), linearly bounded lattice, polytope.  ...  Therefore, the efficient handling of array references in the specifications for image and video processing is crucial for obtaining low cost memory allocation solutions.  ...  As the image polytopes can contain "holes," the equality of the image polytopes is not a proof that the corresponding array references are equivalent.  ... 
doi:10.1109/43.573828 fatcat:syi73xvvzfb6hehgsizkpbmtqm

On the recognition of digital circles in linear time

Peter Sauer
1993 Computational geometry  
For a given object s E R" one can obtain the so-called digitalization dig(s) of s. One problem of the image processing is the recognition of objects s c R", where y = dig(s) is given.  ...  ., On the recognition of digital circles in linear time; Computational Geometry: Theory and Applications 2 (1993) 287-302.  ...  For these reasons we firstly attempt to transform digital circles to digital straight lines and vice versa.  ... 
doi:10.1016/0925-7721(93)90025-2 fatcat:4zohfpmnwbh2zeop5pk3syi3a4

Some theoretical challenges in digital geometry: A perspective

Tetsuo Asano, Valentin E. Brimkov, Reneta P. Barneva
2009 Discrete Applied Mathematics  
The explicit purpose of the present Perspective is to suggest a number of strategic objectives for theoretical research, with an emphasis on the combinatorial approach in image analysis.  ...  In recent years image analysis has become a research field of exceptional significance, due to its relevance to real life problems in important societal and governmental sectors, such as medicine, defense  ...  Acknowledgements The authors are obliged to the two anonymous referees for their useful remarks and suggestions. The authors thank Amy Cuhel-Schuckers and Boris Brimkov for proofreading the text.  ... 
doi:10.1016/j.dam.2009.04.022 fatcat:3nvxwk5u4zhqlagcydyknwejmq

Topological Superfluid Defects with Discrete Point Group Symmetries [article]

Y. Xiao, M. O. Borgh, A. A. Blinova, T. Ollikainen, J. Ruostekoski, D. S. Hall
2022 arXiv   pre-print
In this work we create and verify exotic magnetic phases of atomic spinor Bose-Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope  ...  We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous  ...  ACKNOWLEDGMENTS The authors are grateful for experimental assistance from L. Reuter in obtaining the data presented in Fig. 5  ... 
arXiv:2203.08186v1 fatcat:xvlciiyejbamtb7vwotwedigce

Right-angled Coxeter polytopes, hyperbolic 6-manifolds, and a problem of Siegel [article]

Brent Everitt, John G. Ratcliffe, Steven T. Tschantz
2010 arXiv   pre-print
By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds with Euler characteristic -1 are constructed.  ...  The images in (Z/2) 27 of the side-pairing transformations of Q are the 21 vectors v i = w i +e i , for i = 7, . . . , 27, where w i is the base 2 vector representing the (i−6)th digit of the code for  ...  of Γ n 2 of order 2 n−1 , corresponding to the l n line edges of P n for 2 ≤ n ≤ 7.  ... 
arXiv:1009.3231v1 fatcat:skbajufafzb7ln3kodcceza25i

Digital Analytical Geometry: How Do I Define a Digital Analytical Object? [chapter]

Eric Andres
2015 Lecture Notes in Computer Science  
We will end with open problems and challenges for the future.  ...  We will then explain how, from simple assumptions about properties a digital object should have, one can build mathematical sound digital objects.  ...  I am not quite sure that there exists a corresponding 3D plane thickness (and thus a corresponding general digitization transform) that would dene such digital 3D lines.  ... 
doi:10.1007/978-3-319-26145-4_1 fatcat:y44bugcgrvdmjp4ahfiij7vogm

Linearly constrained Bayesian matrix factorization for blind source separation

Mikkel N. Schmidt
2009 Neural Information Processing Systems  
This transformation ensures, that for any value of y, the corresponding x satisfies the equality constraints.  ...  Task The objective is to factorize the data matrix in order to find a number of source images that explain the data. Ideally, the sources should correspond to the original digits.  ...  From these images we created 4, 000 image mixtures by adding the grayscale intensities of the images two and two, such that the different digits were combined in equal proportion.  ... 
dblp:conf/nips/Schmidt09 fatcat:gsmfzm2rhfgpbhef74pxsgwg4e

A Tutorial on Well-Composedness

Nicolas Boutry, Thierry Géraud, Laurent Najman
2017 Journal of Mathematical Imaging and Vision  
Believing in its prime importance in digital topology, we then propose this state-of-the-art of well-composedness, summarizing its different flavours, the different methods existing to produce well-composed  ...  To get rid of those paradoxes, and to restore some topological properties to the objects contained in the image, like manifoldness, Latecki proposed a new class of images, called wellcomposed images, with  ...  By construction, their connected components are respectively open sets for the miss-transform, and closed sets for the hit-transform.  ... 
doi:10.1007/s10851-017-0769-6 fatcat:pwvvx5rvlndblkexm5tj6y4y7i

Polytopic Planar Region Characterization of Rough Terrains for Legged Locomotion [article]

Zhi Xu, Hongbo Zhu, Hua Chen, Wei Zhang
2022 arXiv   pre-print
This problem is of great importance for terrain mapping in complicated environment and has great potentials in legged locomotion applications.  ...  At the first stage, the planar regions embedded within a sequence of depth images are extracted individually first and then merged to establish a terrain map containing only planar regions in a selected  ...  With labeled pixels in the camera space, a digitized binary image is obtained for each plane. We then extract the boundary of each plane in the camera space.  ... 
arXiv:2207.03098v1 fatcat:n3pdlnesijhxdi3ewjdafbseoe

Combinatorial approach to image analysis

Valentin E. Brimkov, Reneta P. Barneva
2009 Discrete Applied Mathematics  
The focus is on the solution of transformation problems for geometric primitives, especially lines, so that regions of interest can be computed for corresponding geometric features in distinct images.  ...  In the first one, Kristof Teelen and Peter Veelaert present an uncertainty model for geometric transformations based on polygonal uncertainty regions and transformation polytopes.  ... 
doi:10.1016/j.dam.2009.06.030 fatcat:skntxcwdybdvjgohod32jxvixi

Learning a Continuous Hidden Variable Model for Binary Data

Daniel D. Lee, Haim Sompolinsky
1998 Neural Information Processing Systems  
The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images.  ...  A directed generative model for binary data using a small number of hidden continuous units is investigated.  ...  Seung for helpful discussions.  ... 
dblp:conf/nips/LeeS98 fatcat:lx2nuf6e6fdazc3bcg5qzmzogi

Fast penetration depth computation for physically-based animation

Young J. Kim, Miguel A. Otaduy, Ming C. Lin, Dinesh Manocha
2002 Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '02  
It uses bounding volume hierarchies, object-space and image-space culling algorithms to further accelerate the computation and refines the estimated PD in a hierarchical manner.  ...  We demonstrate its application to contact response computation and a time-stepping method for dynamic simulation.  ...  Acknowledgments This research was supported in part by ARO Contract DAAG55-98-1-0322, DOE ASCII Grant, NSF NSG-9876914, NSF DMI-9900157, NSF IIS-982167, NSF ACR-0118743, ONR Contracts N00014-01-1-0067  ... 
doi:10.1145/545265.545266 fatcat:c43zcmxpz5fmlglstehufacr7y
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